Long-term durability of immune responses to the BNT162b2 and mRNA-1273 vaccines based on dosage, age and sex

The lipid nanoparticle (LNP)-formulated mRNA vaccines BNT162b2 and mRNA-1273 are a widely adopted multi vaccination public health strategy to manage the COVID-19 pandemic. Clinical trial data has described the immunogenicity of the vaccine, albeit within a limited study time frame. Here, we use a within-host mathematical model for LNP-formulated mRNA vaccines, informed by available clinical trial data from 2020 to September 2021, to project a longer term understanding of immunity as a function of vaccine type, dosage amount, age, and sex. We estimate that two standard doses of either mRNA-1273 or BNT162b2, with dosage times separated by the company-mandated intervals, results in individuals losing more than 99% humoral immunity relative to peak immunity by 8 months following the second dose. We predict that within an 8 month period following dose two (corresponding to the original CDC time-frame for administration of a third dose), there exists a period of time longer than 1 month where an individual has lost more than 99% humoral immunity relative to peak immunity, regardless of which vaccine was administered. We further find that age has a strong influence in maintaining humoral immunity; by 8 months following dose two we predict that individuals aged 18–55 have a four-fold humoral advantage compared to aged 56–70 and 70+ individuals. We find that sex has little effect on the immune response and long-term IgG counts. Finally, we find that humoral immunity generated from two low doses of mRNA-1273 decays at a substantially slower rate relative to peak immunity gained compared to two standard doses of either mRNA-1273 or BNT162b2. Our predictions highlight the importance of the recommended third booster dose in order to maintain elevated levels of antibodies.

: Model variables and initial conditions for individual and population fits used throughout this work. We simultaneously fit to multiple IgG data sets, where the data sets come from different labs and have arbitrary units (a.u.). We therefore fit an initial condition A given by A 0 . We furthermore simultaneously fit to 4 different interleukin data sets, each having varying responses through time and initial dynamics. We therefore fit the initial condition I 0 .
The initial conditions in this table represent the population initial condition from our fits; every individually-fitted data set may have slightly varying initial dynamics.

Population fit values for two standard doses
The population fit values are determined through a fit to all individual data data sets use for each vaccine dosage regimen. Values and figures for every individual fit for each data set are shown in the following sections.
3 Two standard doses mRNA vaccination of BNT162b2 or mRNA-1273 All individual fits shown in this section were fit simultaneously in Monolix.      3.2 Individual fits to IgG data sets Figure S1: Individual fits to all standard dose IgG data sets used in this work. References for the data set sources can be found in Table 1 of the main text, all individual fitted parameters for each fit can be found in Tables S3 and   S4. 7 3.3 Individual fits to IFN-γ data sets Figure S2: Individual fits to various IFN-γ data sets. References for the data set sources can be found in Table 1 of the main text, all individual fitted parameters for each fit can be found in Tables S3 and S4.
8 Figure S3: Mean IFNγ fit response to the Bergamaschi and Camara data sets. 9 3.4 Individual fits to Interleukin data sets Figure S4: Individual fits to various interleukin data sets. References for the data set sources can be found in Table   1 of the main text, all individual fitted parameters for each fit can be found in Tables S3 and S4. 10 3.5 Goodness of fit predictive checks and parameter distributions  The dashed line represents the median, the blue boxes represent the 25th and 75th percentiles, whiskers extend to extreme data points. Outliers are shown as red crosses.
13 Figure S8: distributions of standardized random effects for all fitted model parameters for the two-dose mRNA data.
The solid black line is an overlaid Guassian distribution.

Two low doses of mRNA-1273 vaccination
Two-low-dose mRNA-1273 data used in this work is sourced from Ref. [10]. This section contains tables summarizing the individual data set fitted parameters.

Model parameter population fits and individual data set fitted values
Data set ID Figure from paper Mateus et al.
Mateus et al.   The full model (Eq.9) was derived following a biologically consistent approach to the immune response upon receiving an LNP mRNA based vaccine. On the surface it appears to be a complex 8 equation coupled model and thus parameter estimation would lead to coupled overfitting complications. However, the model is actually only weakly coupled through an effective activation-inhibition mechanism between plasma B-cells and interleukin.

Individual fits to IgG data sets
We first note the immediate decoupling in the model. The first equations, Eq.9a-c, for L, V , and T are a cascade of linear equations which can be solved in sequence (and analytically). Furthermore, the equation for A depends on, but is decoupled from, B and thus can be solved once the solution for B is independently known, Thus, there are two sets of equations remaining, a coupled system for B and I and a coupled system for C and F .
The parameter fitting in Table S4 demonstrates that the CD8 + cell-mediated removal of IFN-γ is eclipsed by its natural decay rate. This suggests that the term associated to α F C can be ignored. Furthermore, the production of IFN-γ, µ T F is comparable to the decay rate γ F which are both very quick. This suggests a quasi-steady balance of production and decay and that If the CD8 + cell-mediated removal of IF N -γ is small then it is reasonable to suggest that the IFN-γ mediated production of CD8 + cells is also negligible which is supported by the small value of α CF compared to γ C and µ CV in Table S4. This means that the equation for C also decouples and follows a similar solution to that of the CD4 + T-cells, Therefore, with these assumptions our eight equation model really becomes a two equation non-linear coupled system for plasma B-cells and interleukin. However, if we anticipate that the response of the vaccine is mostly transient then we are likely not near the threshold required for saturation effects. This suggests that the parameter s I is not   Table S2.